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Metric regularity, stability and approximations in optimal control

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Abstract:
The talk will consist of the following parts:
1. An informal introduction. General problems that have led to the concept of metric regularity will be briefly discussed.
2. Some basic definitions and theory. Elements of the theory of metric regularity that are relevant to the rest of the talk will be briefly introduced. A version of the main operational tool--a Lyusternik-Graves-type theorem--will be formulated. Then two extensions will be presented: bi-metric regularity and Hölder metric regularity.
3. Metric regularity of optimal control problems. In this part the metric regularity will be translated in the terms of optimal control problems. Error estimates for discretization schemes will be presented as an illustration.
4. Stability and bi-metric Hölder regularity of bang-bang optimal control problems. Although the theory of linear optimal control problems was developed some half a century ago, the ``stability" and the error analyses of discretization schemes for such problems are subjects of recent research. Some new results in this area that involve the material from part 3 will be presented.
5. Metric regularity and approximations of infinite-horizon optimal control problems. The approximation of infinite-horizon optimal control problems that arise in economics is an open and rather challenging issue. Thanks to some recently obtained optimality conditions for such problems it become possible to apply the metric regularity theory and obtain conditions for approximation and stability analysis of infinite-horizon problems. Such will be presented in the final part of the talk.

Type of Seminar:
Optimization and Applications Seminar
Speaker:
Prof. Vladimir Veliov
Institute of Mathematical Methods in Economics Vienna University of Technology, Austria
Date/Time:
May 13, 2013   4:30 pm
Location:

HG G 19.1, Rämistrasse 101
Contact Person:

John Lygeros
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Biographical Sketch:
Vladimir Veliov is Professor and Head of the Research Unit "OR and Control Systems" at the Institute of Mathematical Methods in Economics Vienna University of Technology; on leave from Institute of Mathematics and Informatics Bulgarian Academy of Sciences. His research areas are: optimal control of ordinary and distributed systems; uncertain systems - identification, estimation, control; differential games; operations research and mathematical programming; numerical analysis - approximation, differential equations, optimization; mathematical economics; population dynamics, mathematical epidemiology.